What sum of money at compound interest will amount to 4499.04 in 3 years, if the rates if interest is 3% for the first year, 4% for the second year and 5% for the third year?
Answers
Answer:
Assume here let P = Principal, R%= Rate per annually and Time(T) = n years;
If the interest is compounded for 1 year, then
Amount = P(1+R/100)ⁿ,
Compound Interest = Amount – Principal
= P[(1+R/100)ⁿ – 1]
If Interest is compounded for half yearly(6 months),
then R= R/2 and Time (n) =
2n;
Amount = P(1+R/2 x 100)²ⁿ
If interest is compounded for quarterly, then R= R/4 and n= 4n;
Amount = P (1+ R/4 x 100)⁴ⁿ
If interest is compounded annually but time is in fraction (time = n a/b year),
then
Amount = P (1+R/100)ⁿ x (1+ (a/b)R/100)
If rates of interest areR₁%, R₂%, R₃%for1st, 2nd, 3rd year respectively, then
Amount = P (1 + R₁/100) (1+ R₂/100) (1+R₃/100)
When a borrower pays the sum in parts
(number of instalments = n), (each instalment value = x),
(Total amount paid in instalment A = P (1 + R/100)ⁿ )
Sum P = [x/(1+ R/100) + x/(1+ R/100)² + x/(1+ R/100)³ + ——+ x/(1+ R/100)ⁿ
Example 1: Find the compound interest on Rs 8000/- at 4% pa for 2 years, compounded annually?
Answer:
P= Rs 8000/-, R= 4%pa, Time = 2yr
Amount = P(1+R/100)ⁿ
= 8000 (1 + 4/100)²
= 8000 x 26/25 x 26/25
=Rs 8652.80
Compound Interest = Amount – Principal
= P[(1+R/100)ⁿ – 1]
= 8652.80-8000
= Rs 652.80/-